Alternative to the interpretation by Freund and Schapire [1]}, AdaBoost can be viewed as a form of mirror gradient descent on the exponential loss-function [2]}, [3]}. It is thus natural to expect that it converges to the infimum of the loss-function and eventually interpolates the labels if possible.
In fact, a stronger statement holds: As described in (REF ),
AdaBoost with infinitesimally small learning rate and a growing number of iterations \(T\)  converges to a \(\ell _1\) -margin solution [4]}, [5]}, [6]}.
This holds even non-asymptotically [6]} for many variants of AdaBoost and includes both the exponential and logistic loss-function as well as various choices of adaptive stepsizes \(\alpha _t\) , for instance logarithmic as originally proposed by [1]}, line search [9]}, [5]} or quadratic as in Algorithm REF .
